Helmholtz resonance
From Wikipedia, the free encyclopedia
Helmholtz resonance is the phenomenon of air resonance in a cavity. The device was created in the 1860s by Hermann von Helmholtz to show the height of the various tones. An example of Helmholtz resonance is the sound created when one blows across the top of an empty bottle.
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[edit] Qualitative explanation
When air is forced into a cavity, the pressure inside increases. Once the external force that forces the air into the cavity disappears, the higher-pressure air inside will flow out. However, this surge of air flowing out will tend to over-compensate, due to the inertia of the air in the neck, and the cavity will be left at a pressure slightly lower than the outside, causing air to be drawn back in. This process repeats with the magnitude of the pressure changes decreasing each time.
This effect is akin to that of a bungee-jumper bouncing on the end of a bungee rope, or a mass attached to a spring. Air trapped in the chamber acts as a spring. Air, being compressible, has a definite spring constant. Changes in the dimensions of the chamber adjust the properties of the spring: a larger chamber would make for a weaker spring, and vice-versa.
The air in the port is the mass. Since it is in motion, it possess some momentum. A longer port would make for a larger mass, and vice-versa. The diameter of the port is related to the mass of air and the volume of the chamber. A port that is too small in area for the chamber volume will "choke" the flow while one that is too large in area for the chamber volume tends to reduce the momentum of the air in the port.
[edit] Quantitative explanation
It can be shown[1] that the frequency of the resonance is
,
where v the speed of sound in air. The length of the neck appears in the denominator because the inertia of the air in the neck is proportional to the length. The volume of the cavity appears in the denominator because the spring constant of the air in the cavity is inversely proportional to its volume. The area of the neck matters for two reasons. Increasing the area of the neck increases the inertia of the air proportionately, but also decreases the velocity at which the air rushes in and out.
[edit] Applications
Helmholtz resonance finds application in internal combustion engines (see airbox), subwoofers and acoustics. In stringed instruments, such as the guitar and violin, the resonance curve of the instrument has the Helmholtz resonance as one of its peaks, along with other peaks coming from resonances of the vibration of the wood.
